Question

5 rewrite the following statement as an if - then conditional: all linear pairs are supplementary. linear pairs are complementary. if a pair of angles sum to 90°, then they are supplementary. all linear pairs are not supplementary. if a pair of angles sum to 180°, then they are supplementary. 6 is the following statement a definition, postulate, or theorem? if m is the midpoint of a line segment ab, then am = 0.5ab and mb = 0.5ab theorem definition postulate 7 is the following statement a definition, postulate, or theorem? vertical angles are congruent. theorem definition postulate

Explanation:

Question 5

A linear pair of angles is formed when two adjacent angles form a straight line. The sum of angles on a straight line is \(180^{\circ}\), and supplementary angles are defined as two angles whose sum is \(180^{\circ}\).

A definition is a statement that precisely describes the meaning of a term. The mid - point of a line segment \(AB\) is defined as a point \(M\) such that \(AM = 0.5AB\) and \(MB=0.5AB\). It is not a theorem (which requires proof) or a postulate (an accepted statement without proof in a different context).

A theorem is a statement that can be proven. The statement “Vertical angles are congruent” can be proven using the properties of angles and lines. A definition would be a statement that tells what vertical angles are (e.g., two non - adjacent angles formed by two intersecting lines). A postulate is an accepted fact without proof, and this statement is proven.

Answer:

If a pair of angles sum to \(180^{\circ}\), then they are supplementary.

Question 6